How To Convert Ln To Log 10

The logarithm of a number is the power to which the base must be raised in order to obtain this number; for example, the logarithm of 25 with the base 5 is 2 since 5² equals 25. "Ln" stands for the natural logarithm that has the Euler's constant, approximately 2.71828, as the base. Natural logarithms have many uses in the sciences as well as pure math. The "common" logarithm has 10 as its base and is denoted as "log." The following formula allows you to take the natural logarithm by using the base-10 logarithm:

\(\ln(\text{number}) = \frac{\log(\text{number})}{\log(2.71828)}\)

Before you take the logarithm of a number, check its value. Logarithms are defined only for numbers greater than zero, i.e. positive and nonzero. The result of a logarithm, however, may be any real number – negative, positive or zero.

Enter the number you want to take the logarithm of on your calculator. Press the button "log" to calculate the common log of the number. For example, to find the common log of 24, enter "24" on your calculator and press the "log" key. The common log of 24 is 3.17805.

Enter the constant "e" (2.71828) on your calculator and press the button "log" to calculate log₁₀:

\(\log_{10}(2.71828 ) = 0.43429\)

Divide the common log of the number by the common log of e, 0.43429, to find the natural logarithm via the common log. In this example:

\(\ln(24) = \frac{1.3802}{0.43429} = 3.17805\)